A UN spokesman said policemen raided a UN warehouse on Tuesday after officials refused to hand over the aid to a Hamas-controlled ministry.
The UN said it was the first time its aid had been confiscated by Hamas.
It condemned the action and demanded the goods be immediately returned. Hamas denied its men had taken any aid.
UN spokesman Christopher Gunness said Hamas police took 3,500 blankets and over 400 food parcels.
The Hamas Social Affairs Minister in Gaza, Ahmed al-Kurd, denied that members of the Islamist movement had removed aid from a UN building.
However, he said his ministry was in dispute with the UN relief agency about how aid should be distributed.
He accused the UN of giving aid to local groups with ties to Hamas opponents.
Reconstruction plan
About half the population in the Gaza Strip are dependent on UN food aid, since Israel imposed a blockade on the territory 19 months ago.
Aid delivery became increasingly difficult during Israel's offensive against Hamas which began in late December.
The UN said it has increased its food distribution to cover 900,000 of Gaza's population of 1.5 million.
However, the UN, along with most of the Western world, does not deal directly with Hamas, which controls the Gaza Strip.
Meanwhile, the Palestinian Authority (PA) has announced $600m (£417m) for reconstruction in the Gaza Strip.
PA Prime Minister Salam Fayyad said the programme would cover all Palestinian houses destroyed or damaged during Israel's 22-day offensive in December and January.
"The amount of the project is $600 million. Most of it will come from donors," Mr Fayyad said in a speech in the West Bank city of Ramallah.
The Palestinian Authority would contribute $50m of its own money to the to assist Gazans, he said.
Further details would be announced later, he added.
Initial Palestinian estimates said rebuilding would cost $2bn (£1.4bn) and take three to five years.
Meanwhile Palestinian leader Mahmoud Abbas, speaking to the European Parliament in Strasbourg on Wednesday, said he would push for a war-crimes investigation into Israel's attacks.
"People who committed those crimes have to be held responsible so that these crimes cannot be repeated," he told reporters after a speech which garnered a standing ovation.
"We are stretching out our hand for peace with Israel. But what was done is regretfully crimes of war."
He denounced Hamas' rocket attacks into Israel, but said "our doors are still open" for a unity government with the militant group.
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